William Monckton-Arundell, 2nd Viscount Galway (c. 1725 – 18 November 1772) was an English peer and politician.

He was born c. 1725, the eldest surviving son of John Monckton, 1st Viscount Galway and the elder brother of Lieutenant-General Robert Monckton, Governor of New York.

William was educated at Westminster School and succeeded his father as Viscount Galway in July 1751.

His inheritance included the Grade I listed Serlby Hall in Nottinghamshire.

In 1769 he inherited further estates from his maternal aunt, Lady Frances Arundell of Allerton Mauleverer, adopting the additional surname of Arundell in accordance with the terms of her will.